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The fundamental issue of quality-of-service (QoS) routing has triggered a lot of research during the last few years. However, the proposed algorithms attempt to route communication demands only on a call by call basis, without taking into account future traffic. There are nonetheless cases where the traffic profile is known. In this paper, we address this related problem to QoS routing, more specifically, the off-line planning of bandwidth allocation to demands known in advance. Shortest-path routing is the traditional technique applied to this problem. However, this can lead to poor network utilization and even congestion. We show how an abstraction technique combined with systematic search algorithms and heuristics derived from artificial intelligence make it possible to solve this problem more efficiently and in much tighter networks, in terms of bandwidth usage. In addition, this abstraction technique also allows to explain during search why some allocation problems are indeed infeasible. Then, the network regions between which bandwidth must be added are then identified.